Multiply the following complex numbers: $({5-5i}) \cdot ({-4})$
Explanation: Complex numbers are multiplied like any two binomials. First use the distributive property: $ ({5-5i}) \cdot ({-4}) = $ $ ({5} \cdot {-4}) + ({5} \cdot {0}i) + ({-5}i \cdot {-4}) + ({-5}i \cdot {0}i) $ Then simplify the terms: $ (-20) + (0i) + (20i) + (0 \cdot i^2) $ Imaginary unit multiples can be grouped together. $ -20 + (0 + 20)i + 0i^2 $ After we plug in $i^2 = -1$ , the result becomes $ -20 + (0 + 20)i - 0 $ The result is simplified: $ (-20 - 0) + (20i) = -20+20i $